In this paper, we introduce a novel cooperative target tracking algorithm, namely the quantum-inspired belief propagation, aimed at rectifying the limitations observed in existing localization algorithms employed in multi-target cooperative tracking scenarios. Leveraging the principles of quantum superposition, our algorithm seeks to alleviate the uncertainty inherent in message fusion within belief propagation frameworks, thereby enhancing the accuracy and stability of multi-target cooperative localization. The utilization of the quantum Monte Carlo method facilitates the simulation of the message distribution process, with quantum particles embodying the superposition of multiple states concurrently. This approach effectively addresses the intractable integrations encountered in message updating on factor graphs, rendering the algorithm agnostic to the number of particles involved. Moreover, quantum unitary transformations and quantum black-box operations are deployed to encode factor graph function nodes for the propagation of quantum messages. This innovation surmounts the challenge posed by traditional factor graph function nodes’ inability to process quantum messages. Experimental findings corroborated the superiority of the proposed algorithm in terms of accuracy and robustness.

Abrupt-motion tracking is challenging due to the target’s unpredictable action. Although particle filter is suitable for target tracking of nonlinear non-Gaussian systems, it suffers from the problems of particle impoverishment and sample-size dependency. Inspired by quantum mechanics that one quantum bit could represent a superposition of two states, this paper proposes a diversity-preserving quantum-enhanced particle filter (DQPF). Firstly, we quantized the motion modes of particles into a superposition of several modes of motion, resulting in a quantum particle set that retains diversity. Aiming for the abruption of target motion, we propagate the quantum particles during the prediction stage. The quantum particles will already be in these possible positions even if abruption occurs, which addresses the abrupt-motion issue and reduces the tracking delay. Benefitting from quantum mechanics, the proposed particle filter has better precision and stability with fewer particles than the general particle filter. Compared to state-of-the-art, numerical experimental results demonstrate that the proposed DQPF has higher accuracy and stability under the same conditions, displaying superior performance to traditional modified particle filter methods.

Cooperative localization is essential for many Internet of Things (IoT)-related applications in harsh environments. Generally, the inertial navigation system is self-contained and adopted as the basis of a cooperative tracking system, but it still faces the problem of accumulated errors and cannot provide long-term, high-precision positioning. The particle filter (PF) is widely used to fuse multiple information to inhibit accumulative errors. However, particle degradation and impoverishment remain unsolved. This article proposed an IMU/time-of-arrival (TOA) fusion-based tracking method, namely, uncertainty-constrained belief propagation (UCBP). We address particle degradation and impoverishment by introducing uncertainty-constrained optimization into belief propagation (BP). An uncertainty-constrained resampling (UCR) method is applied to quantify the uncertainty in cooperative systems. Hierarchical resampling is realized to solve the particle impoverishment issue. Meanwhile, particle degradation is resolved through constrained resampling while ensuring the diversity of particles. Furthermore, we illustrated the factor graph (FG) structure of UCBP to mitigate the accumulation of errors through message fusion over the graph. Compared with the state-of-the-art methods, our proposed UCBP algorithm has better precision and robustness without introducing much time overhead.